In this paper we give the q-analogue of the higher-order Bessel operators
studied by I. Dimovski [3],[4], I. Dimovski and V. Kiryakova [5],[6], M. I.
Klyuchantsev [17], V. Kiryakova [15], [16], A. Fitouhi, N. H. Mahmoud and
S. A. Ould Ahmed Mahmoud [8], and recently by many other authors.
Our objective is twofold. First, using the q-Jackson integral and the
q-derivative, we aim at establishing some properties of this function with
proofs similar to the classical case. Second, our goal is to construct the
associated q-Fourier transform and the q-analogue of the theory of the heat
polynomials introduced by P. C. Rosenbloom and D. V. Widder [22]. For
some value of the vector index, our operator generalizes the q-jα
Bessel operator of the second order in [9] and a q-Third operator in [12].